I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.

I need to find:
the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
and the lim as x goes to zero of the same function

Please help!

Aug 31st 2006, 06:10 AM

galactus

When taking the limit of a rational expression, if x approaches +/- infinity, you can disregard all but the coefficients of the highest powers.

Therefore you have,

Now, you can see what it is?.

As x approaches 0, look close, can you see it?.

Aug 31st 2006, 06:39 AM

ThePerfectHacker

Quote:

Originally Posted by afn2

I need to find:
the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
and the lim as x goes to zero of the same function

Divide the numerator and denominator by
The numerator is,
The denominaot is,
Since both limits exists thus the value of the limit is 3/4

Aug 31st 2006, 06:57 AM

topsquark

Quote:

Originally Posted by afn2

I need help solving what I think is a pretty simple limits questions, but I just can't see where to start.

I need to find:
the lim as x goes to infinity of (3x^2+2x+2)/(4x^2+2x+7)
and the lim as x goes to zero of the same function

Please help!

The limit as x goes to 0 should be simple. Both the numerator and denominator are continous functions on all real numbers (ie. the domain in both cases is all real numbers) and the denominator is not 0 for x = 0, so effectively all you need to do is substitute 0 for x in the expression.

-Dan

Aug 31st 2006, 07:50 AM

afn2

Thanks a bunch, I knew it was pretty simple, but I've always struggled with limits, even though I completely get derivatives and integrals. I just needed a push in the right direction. Thanks guys!